查询词典 plano convex

The model for calculating the stability of the resonator containing a laser rod with curvature ends was developed,which was based on the transfer matrix theory of Gauss beam. The results from the numerical simulations on some typical resonators indicate that the laser rod with curvature ends can expand the stable region of plano-plano,plano-concave and plano-convex cavity notability;despite the laser rod with curvature ends can improve the stability of above mentioned cavities,it costs the effective mode volume.

计算结果表明，对于几类典型的谐振腔如平平腔、平凹腔，球面端面激光棒可以显著的扩展强热聚焦作用下的稳定工作范围；球面端面激光棒在提高约束稳定性和热稳定性的同时，通常是以牺牲有效模式体积为代价的。

Two He-Ne lasers have been designed in experiment,one with simplest 2D axisymmetric folded-combined cavity that are composed of a concave-plano-concave folded cavity and a plano-concave cavity , and other with simplest 3D axisymmetric folded-combined cavity that are composed of two concave-plano-concave folded cavities and a plano-concave cavity.

本文实验设计了由一个凹-平-凹折迭腔与一个平凹腔组合的二维轴对称折迭-组合腔型He-Ne激光器及由两个凹-平-凹折迭腔与一个平凹腔组合的最简单立体轴对称折迭-组合腔型He-Ne激光器。

This article outlines the progress of ancient Chinese lenses from the Pre-Qin Period to the Five Dynasties, and discusses mainly two arguments: First, the"yangsui" recorded and narrated in Lun Heng by Wang Chong of Eastern Han Dynasty may be a plano-convex glass lens; secondly, the"four mirrors" recorded and narrated in Tanzi Hua Shu by Tan Qiao of Southern Tang Dynasty may be a plano-convex lens, a biconvex lens, a transparent planeparallel plate and a concave-convex lens respectively, but what kind of tra...

本文概述了中国古代透镜从先秦到五代的发展进程，着重从古代文献和出土文物的研究出发，结合中国古代社会经济发展水平，论证了东汉王充《论衡》中记述的阳燧可能是玻璃平凸透镜；论证了南唐谭峭的《谭子化书》中记述的"四镜"可能是平凸透镜、双凸透镜、平光镜和凹凸透镜。作者认为《谭子化书》"四镜"段可能实际上是对中国古代透镜发展的阶段性总结。

This article outlines the progress of ancient Chinese lenses from the Pre-Qin Period to the Five Dynasties, and discusses mainly two arguments: First, the"yangsui" recorded and narrated in Lun Heng by Wang Chong of Eastern Han Dynasty may be a plano-convex glass lens; secondly, the"four mirrors" recorded and narrated in Tanzi Hua Shu by Tan Qiao of Southern Tang Dynasty may be a plano-convex lens, a biconvex lens, a transparent planeparallel plate and a concave-convex lens respectively, but what kind of tra...

本文概述了中国古代透镜从先秦到五代的发展进程，着重从古代文献和出土文物的研究出发，结合中国古代社会经济发展水平，论证了东汉王充《论衡》中记述的阳燧可能是玻璃平凸透镜；论证了南唐谭峭的《谭子化书》中记述的&四镜&可能是平凸透镜、双凸透镜、平光镜和凹凸透镜。作者认为《谭子化书》&四镜&段可能实际上是对中国古代透镜发展的阶段性总结。

At the beginning of this thesis, the author gives the definition and the equivalent definition of convex function, and then proves the equivalent relationship between them. Secondly the author proposes the decision theorem of convex function which provides a judgment basis of whether a function is a convex function. Thirdly the author summarizes and proves the convex function's operational, basic, differential and integral property. Finally the author proves several famous convex function inequalities, such as Jensen inequality, Holder inequality, Cauchy inequality. The author also provides the application of these inequalities and illustrates the importance of convex function's basic inequality and integral property in the proving process.

本文开始给出了凸函数的定义及等价定义，并证明了它们之间的等价关系；接着提出了凸函数的判定定理，对一个函数是否是凸函数提供判断依据；然后对凸函数的运算性质、基本性质、微分性质、积分性质四个方面的性质进行了总结，并给予了证明；最后证明了凸函数的几个著名不等式詹森不等式、赫尔德不等式、柯西不等式，给出了这几个不等式的一些应用实例，并举例说明凸函数的基本性质和积分性质在不等式证明过程中的重要作用。

At the beginning of this thesis, the author gives the definition and the equivalent definition of convex function, and then proves the equivalent relationship between them. Secondly the author proposes the decision theorem of convex function which provides a judgment basis of whether a function is a convex function. Thirdly the author summarizes and proves the convex function's operational ,basic , differential and integral property. Finally the author proves several famous convex function inequalities, such as Jensen inequality, Holder inequality, Cauchy inequality and Minkowski inequality. The author also provides the application of these inequalities and illustrates the importance of convex function's basic inequality and integral property in the proving process.

本文开始给出了凸函数的定义及等价定义，并证明了它们之间的等价关系；接着提出了凸函数的判定定理，对一个函数是否是凸函数提供判断依据；然后对凸函数的运算性质、基本性质、微分性质、积分性质四个方面的性质进行了总结，并给予了证明；最后证明了凸函数的几个著名不等式詹森不等式、赫尔德不等式、柯西不等式和闵可夫斯基不等式以及这几个不等式的应用，并举例说明凸函数的基本性质和积分性质在不等式证明过程中的重要作用。

The convex function develeped so many years that convex functionals are now a class of very universal functionals.The kinetic energy in the classical is the most natural convex function.Others like entropy and so on are convex functions.The economic core is closely connected with the convex function.The western economic core question is the optimized question.The optimized theory has something to do with the convex function and the concave function.

凸函数的发展经年已相当完善其应用非常广泛，在古典力学中的动能，就是最自然直接的凸函数，其他如熵……等均是，连经济学的核心都与之有极密切相关，西方经济学的核心问题是最优化问题，最优化理论又与凸函数与凹函数密切相关。

Lens, plano-convex lens, double-convex lens, plano-concave lens, double-concave lens, plus/minus Meniscus Lens.

球面镜：平凸透镜、双凸透镜、平凹透镜、双凹透镜、正/负弯月透镜、超半球透镜、金属球面镜、积分器及其他球面胶合镜等。

As far as I know there are three kinds fo such tests commonly exist - the Dall Null test which uses a single plano-convex lens, an auto-collimating test uses a flat as big as the mirror under test and Offner test using two plano convex lens.

据我所知现时一般存有3种此类测试，其一是达耳零位测试采用单一只平凸透镜，再有是自准直测试采用一块平镜大小一如被测试的反射镜，及 Offner 测试采用2只平凸透镜。

Chapter 4 establishes the theory of convex fuzzy mappings: The concepts, such as Jensen's inequality, positively homogeneous, infimal convolution, right scalar multiplication and convex hull are introduced. The corresponding theorems are demonstrated by using the parametric representations of fuzzy numbers. In anti-fuzzy number space, the conjugate mapping of convex fuzzy mapping is concerned, and convexities of conjugate set and conjugate mapping of convex fuzzy mapping are proved. The notions of subgradient, subdifferential, differential with respect to convex fuzzy mappings are investigated, which provides the basis of the theory of fuzzy extremum problems.

在第4章中，建立了有关凸模糊映射的理论：建立了关于凸模糊映射的Jensen不等式、模糊正齐次映射、凸模糊映射的下卷积、右数乘和凸包等概念，利用模糊数的参数化表示，给出了相应的定理；在反模糊数空间，对凸模糊映射的共轭也作了探讨，证明了凸模糊映射的共轭集合和共轭映射都是凸的；最后对凸模糊映射的次梯度、次微分和微分等概念进行了研究，为模糊极值理论打下了基础。

The circulation, consumption and reproduction of the trilogy have not only testified to its historical significance and literariness, but also invested it with new meanings.

该三部曲的流通、消费与再生产不仅验证了其历史意义及文学性，而切还赋予它以新的意义。

If he thought that he could buy me off, he would be wrong.

如果他认为他可以收买我，那他就大错特错了。